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In stimulated emission, why don't electrons just jump to a higher energy level instead of a lower one when they absorb a photon for the second time? Isn't that counter intuitive?

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    $\begingroup$ They don't jump down when absorbing- they jump down when the 'wave' stimulates emission. Further, two-photon absorption does occur in special situations. $\endgroup$ – Carl Witthoft Mar 13 at 15:18
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why don't electrons just jump to a higher energy level

They can't, because energy needed for jumping into a second energy level is different than that of incoming photon. There may be some exceptions such as multi-photon absorption involving an intermediate virtual energy level, however the probability of such processes is low compared to single-photon absorption. Thus, simply energy band of higher level does not fit the one which the incoming photon has: $\Delta E_{2\to3} \neq h\nu$.

when they absorb a photon for the second time

This is actually wrong. Atoms DO NOT absorb incoming photons a second time as I've explained previously; they can't do it, because the system is already in an inverted state - where many of atoms are excited and not in ground state. Thus such material in an inverted state is basically transparent for incoming photons.

Why does stimulated emission happen?

This simple question has no easy answer. We need deep quantum mechanics and quantum electrodynamics framework knowledge to explain this. However, if this question would be attacked on intuitive level, I would explain that like this:

Already excited atoms become "unstable", in the sense that there's a spontaneous emission underway, so any event can force an atom to go back to ground level. It's like when at top of mountain is a lot of snow which has a lot of potential energy, waiting to be released, and it's enough for a small perturbation, like strong sound, skier, etc., to start a snow avalanche effect. Then falling snow will touch other volumes of snow and process repeats, until huge amounts of snow reach the ground.

Same for stimulated emission. An incoming photon "shakes" an excited atom, which then emits duplicated photon, which in turn shakes other atom, and process repeats further inducing stimulated emission avalanche, until all excited atoms go back to ground state. But then they are excited again by an external light source or by other means, and the overall process repeats producing a stable laser beam.

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    $\begingroup$ Two-level lasing system is impossible. You won't get a "stable laser beam" this way. Also, the analogy with a snow avalanche is bad because stimulated emission only happens as a resonance event: it requires a well-frequency-matched photon to happen—unlike snow avalanche, which can happen due to any perturbation, without any resonance. $\endgroup$ – Ruslan Mar 13 at 19:28
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    $\begingroup$ I could not find a better analogy to explain in "down-to-earth" simple way. You are welcome to find your own better analogy and post it as an answer here. No need for negative critics. $\endgroup$ – Agnius Vasiliauskas Mar 13 at 19:37
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    $\begingroup$ "No need for negative critics" – no need to feel offended by mere criticism. It's not even a downvote ;) . But if a post is (even partially) wrong in my opinion, then I as a member of this community feel the need to comment on this wrongness, so that the author could fix it or explain why it's not wrong. I think it's better than a silent downvote. $\endgroup$ – Ruslan Mar 13 at 19:46
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    $\begingroup$ The point is that every analogy is questionable and should not be taken as granted, but merely as a way to broaden your physical intuition. If you want exact mechanism operating - you need to study this field exactly with required math apparatus. No analogy will help at this point. However a lot of people here comes without good physics background, so analogies to them must be made at a "very accessible" level. Sacrificing exact mechanism details. Your right to down-vote of course, but also your right to post a better analogy,- in this way community will get a lot more benefits. $\endgroup$ – Agnius Vasiliauskas Mar 13 at 19:54
  • $\begingroup$ But it’s also okay to comment the place where the analogy breaks down. This way the readers are made aware of the limitations. $\endgroup$ – Superfast Jellyfish Mar 14 at 9:28
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why don't electrons just jump to a higher energy level

The answer is easy, for the electron in the excited state to jump up one step would mean that the photon coming in has the frequency/energy needed for that jump, which is improbable, because the energy level differences cannot be the same. Look here . And even if in some molecular states this could be true, one would not choose those molecules to study stimulated emission.

This type of "resonance" is described mathematically in the link, and pictorially:

stimem

Here is an answer for modeling stimulated emission in QED

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    $\begingroup$ It reminds me a question from my laser physics course: "why can't one make a laser out of a harmonic oscillator?" $\endgroup$ – Vadim Mar 13 at 8:29
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    $\begingroup$ @Vadim yeah, and this answer unfortunately doesn't address this. (Well, some of the links might, but then this would be a link-only answer.) $\endgroup$ – Ruslan Mar 13 at 8:48
  • $\begingroup$ @Ruslan I think the answer is built around the same idea: if the distances between the energy levels were the same, we would have more stimulated absorption than stimulated emission, because the energy spectrum is bounded from the bottom. $\endgroup$ – Vadim Mar 13 at 8:54
  • $\begingroup$ well, I was thinking of atoms, not harmonic oscillation solutions. The question is about lasers. $\endgroup$ – anna v Mar 13 at 9:37
  • $\begingroup$ Why doesn't the atom simply absorb enough energy to jump up to the next energy level, leaving the rest as a lower-energy photon? $\endgroup$ – Sean Mar 13 at 21:25

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